Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 20 Page 73

The measures of complementary angles add up to 90^(∘).

∠ ADB and ∠ BDC

Practice makes perfect
Let's start by recalling the definition of complementary angles.

Complementary Angles

Two positive angles whose measures have a sum of 90^(∘).

Now, let's consider the given diagram.

There is one angle which is marked with a square — ∠ CDA. This means it is a right angle and its measure is 90 ^(∘). ∠ CDA is the sum of angles ∠ ADB and ∠ BDC, so the sum of measures of these angles has to add up to 90 ^(∘). This means that they are complementary.